Show the Proof

import proveit
# Automation is not needed when only showing a stored proof:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%show_proof

	step type	requirements	statement
0	instantiation	1, 2, 3, 4, 5	, , , , ,  ⊢
	: , : , : , : , :
1	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.doubly_scaled_as_singly_scaled
2	instantiation	6, 26, 8, 9	⊢
	: , : , :
3	instantiation	7, 26, 8, 9, 10, 11, 12, 13	, , ,  ⊢
	: , : , : , :
4	instantiation	47, 32, 14	⊢
	: , : , :
5	instantiation	47, 32, 15	⊢
	: , : , :
6	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_of_vec_spaces_is_vec_space
7	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_is_in_tensor_prod_space
8	instantiation	17	⊢
	: , : , :
9	instantiation	16, 26	⊢
	:
10	instantiation	17	⊢
	: , : , :
11	instantiation	20, 21, 18	⊢
	: , : , :
12	instantiation	20, 21, 19	,  ⊢
	: , : , :
13	instantiation	20, 21, 22	⊢
	: , : , :
14	assumption		⊢
15	assumption		⊢
16	theorem		⊢
	proveit.linear_algebra.complex_vec_set_is_vec_space
17	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
18	assumption		⊢
19	instantiation	23, 24	,  ⊢
	:
20	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
21	instantiation	25, 26, 27	⊢
	: , : , :
22	assumption		⊢
23	assumption		⊢
24	instantiation	28, 29, 30	⊢
	:
25	theorem		⊢
	proveit.logic.sets.cartesian_products.cart_exp_subset_eq
26	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
27	instantiation	31, 32	⊢
	: , :
28	theorem		⊢
	proveit.numbers.number_sets.integers.nonneg_int_is_natural
29	instantiation	47, 33, 45	⊢
	: , : , :
30	instantiation	34, 35	⊢
	: , :
31	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
32	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
33	instantiation	36, 43, 44	⊢
	: , :
34	theorem		⊢
	proveit.numbers.ordering.relax_less
35	instantiation	37, 38, 39	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
37	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
38	instantiation	40, 41	⊢
	:
39	instantiation	42, 43, 44, 45	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
41	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
42	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
43	instantiation	47, 48, 46	⊢
	: , : , :
44	instantiation	47, 48, 49	⊢
	: , : , :
45	assumption		⊢
46	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
47	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
48	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
49	theorem		⊢
	proveit.numbers.numerals.decimals.nat4